The function \(Q^P\)  is the ratio of correctly identified pairs of links, and so \(0 \le Q^P(\mathcal {P}) \le 1\) . Its additivity is proved using \(q^P(\mathcal {C}) = \frac{1}{n(n-1)}\sum _{u \in \mathcal {C}} |\lbrace v \in \mathcal {C}, \lbrace u,v\rbrace  \in E\rbrace | + |\lbrace v \notin \mathcal {C}, \lbrace u,v\rbrace  \notin E\rbrace |\) . This quality function can be computed in \(\mathcal {O}(m)\)  and may be generalized to weighted graph as discussed in [1]}.
